Causal Effects and Experiments

GVPT399F: Power, Politics, and Data

Causes and effects

Our goal is to better understand what factors lead to certain outcomes of interest.

  • Does increasing the number of voting booths close to a potential voter make that person more likely to vote?

  • Do peace treaties signed with factionalized rebel groups more often lead to a return to conflict than those signed with a single, cohesive group?

  • Does trade between two countries make war between them less likely?

Causes and effects

These are causal statements:

  • More local voting booths \(\rightarrow\) More likely to vote

  • More factionalization \(\rightarrow\) More likely to restart conflict

  • Trade \(\rightarrow\) Less likely to go to war

How to identify causes and their effects

Proving that changes to one factor cause changes to another is very tricky!

  • Need to account for all the other factors

The efficacy of international election monitors

Do international monitors cause less election-day fraud in democratic elections?

  • Number of elections monitored by international observers exploded throughout the 2000s

  • But do monitors increase the chances the election will be free and fair?

  • In other words, are they effective?

The efficacy of international election monitors

Dr Susan Hyde set out to answer this very question. From her article (page 39):

If the presence of international observers causes a reduction in election-day fraud, the effect of observers should be visible at the subnational level by comparing polling stations that were visited by observers with those that were not visited. More specifically, if international monitoring reduces electionday fraud directly, all else held equal, the cheating parties should gain less of their ill-gotten vote share in polling stations that were visited by international monitors.

Causal relationships

Refers to the directional connection between a change in one variable and a corresponding change in another.

  • The direction matters!

  • Treatment variable: the variable causing changes to another variable.

  • Outcome variable: the variable changing as a result of changes to another variable (the treatment).

Treatment and outcome variables

We want to test whether the presence of international monitors (treatment) leads to less election day fraud (outcome).

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station

Treatment variable

At any given polling station in any given election, monitors may be: 1) present, or 2) not present.

Two different conditions:

  • Treatment: condition with treatment (monitors are present)

  • Control: condition without treatment (monitors are not present)

Outcome variable

At any given polling station in any given election, fraud may: 1) occur, or 2) not occur.

Observing our outcome

Sometimes it can be hard to observe our outcome of interest.

  • How might we see all election-day fraud?

  • How might we measure it?

Observing our outcome

Hyde’s answer: vote-share!

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station \(\rightarrow\) Lower vote-share for the cheating party

Individual causal effects

We want to know whether the treatment causes a change in our outcome of interest.

What might this look like in the real world?

  • Imagine we are looking at a specific election

  • Five polling stations

Parallel worlds

Hypothetical election

ID Monitored vote % Non-monitored vote %
1 38.24 97.43
2 31.34 81.38
3 43.31 75.49
4 40.18 68.51
5 54.88 89.31

Individual effects

The only difference between these two conditions is the presence of international monitors!

  • The difference between vote shares under these conditions is caused by the monitors.

Individual effects

ID Monitored vote % Non-monitored vote % Difference (%)
1 38.24 97.43 -59.19
2 31.34 81.38 -50.04
3 43.31 75.49 -32.18
4 40.18 68.51 -28.33
5 54.88 89.31 -34.43

No parallel worlds

Sadly for us, we cannot create parallel worlds…

What now?

ID Monitored Monitored vote % Non-monitored vote % Difference
1 1 38.24 NA NA
2 1 31.34 NA NA
3 1 43.31 NA NA
4 0 NA 68.51 NA
5 0 NA 89.31 NA

Average causal effects

We need to move away from looking at individuals and start to look for patterns in our group.

Back to our parallel worlds

ID Monitored vote % Non-monitored vote % Difference
1 38.24 97.43 -59.19
2 31.34 81.38 -50.04
3 43.31 75.49 -32.18
4 40.18 68.51 -28.33
5 54.88 89.31 -34.43

Difference of averages across all individuals

What was the average vote share received in each world?

Avg. monitored vote % Avg. non-monitored vote % Difference
41.59 82.42 -40.83

Back to reality

ID Monitored Monitored vote % Non-monitored vote % Difference
1 1 38.24 NA NA
2 1 31.34 NA NA
3 1 43.31 NA NA
4 0 NA 68.51 NA
5 0 NA 89.31 NA

Difference-of-means

What was the average vote share received in each group?

Avg. monitored vote % Avg. non-monitored vote % Difference
37.63 78.91 -41.28

How on Earth does this work so well?

Randomization!

  • Monitors were assigned to polling stations randomly (for example, with the flip of a coin)

  • This created two groups of stations that were roughly identical on average to one another prior to treatment

  • This mimics what happens when we split our world into two (creating two literally identical groups)

Our goal

We want two groups that are completely identical to one another prior to treatment.

  • This allows us to compare their outcomes after treatment and claim that the treatment caused differences in those outcomes (if any differences exist)

Our goal

Next best thing

Instead, we should try to make two groups that are as similar as possible to each other prior to treatment.

The magic of randomization

Perfectly random assignment does this very well!

Don’t take my word for it

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Our group

ID Height Weight Eye colour
1 168.09 88.99 Blue
2 167.65 79.18 Brown
3 177.98 57.43 Grey
4 165.78 75.69 Green
5 169.25 88.53 Grey
6 168.13 69.16 Green
7 163.46 82.53 Grey
8 162.71 63.50 Green
9 162.37 79.47 Grey
10 167.73 78.13 Blue
11 183.98 90.12 Blue
12 170.65 80.77 Grey
13 172.10 100.08 Green
14 164.96 75.34 Brown
15 168.50 93.14 Brown
16 178.37 85.26 Grey
17 170.71 84.51 Blue
18 171.52 70.54 Grey
19 174.60 81.44 Green
20 168.50 90.35 Grey
21 168.14 60.92 Grey
22 164.56 85.65 Grey
23 169.44 72.09 Grey
24 180.33 75.69 Brown
25 169.95 86.88 Brown
26 177.57 88.34 Green
27 169.01 70.70 Green
28 176.60 93.62 Blue
29 165.24 76.34 Green
30 165.62 66.87 Grey
31 180.71 83.29 Blue
32 167.76 72.33 Green
33 157.26 71.70 Blue
34 156.54 103.45 Blue
35 165.18 80.55 Green
36 168.49 81.54 Grey
37 160.43 60.27 Grey
38 178.23 75.10 Green
39 180.80 94.18 Grey
40 178.17 100.40 Blue
41 173.13 83.90 Blue
42 169.71 74.63 Blue
43 172.65 91.93 Grey
44 174.95 88.44 Blue
45 170.61 79.57 Brown
46 165.23 90.13 Grey
47 176.94 80.02 Green
48 160.80 76.57 Blue
49 165.69 73.29 Blue
50 167.15 82.52 Blue
51 176.00 68.63 Grey
52 165.45 82.08 Green
53 156.10 89.26 Grey
54 175.13 71.62 Blue
55 153.53 81.37 Brown
56 169.54 81.90 Green
57 165.12 79.77 Blue
58 157.54 83.71 Green
59 160.74 77.19 Grey
60 161.55 90.73 Brown
61 171.25 64.53 Brown
62 169.39 83.20 Brown
63 175.46 90.05 Brown
64 165.66 88.24 Blue
65 154.86 91.06 Brown
66 175.14 79.75 Grey
67 159.96 70.15 Blue
68 179.79 83.41 Green
69 164.54 85.69 Grey
70 174.96 83.22 Green
71 164.30 92.07 Brown
72 177.54 69.04 Brown
73 176.04 87.41 Brown
74 170.89 83.72 Grey
75 158.89 78.55 Grey
76 164.74 69.47 Grey
77 161.98 101.60 Grey
78 169.34 68.99 Brown
79 169.99 93.26 Grey
80 164.39 71.53 Green
81 174.02 90.99 Brown
82 171.57 80.53 Grey
83 171.25 83.25 Blue
84 174.18 75.49 Blue
85 171.26 73.02 Green
86 166.76 91.66 Green
87 172.64 71.37 Blue
88 167.76 75.99 Green
89 167.86 60.90 Grey
90 167.38 98.61 Brown
91 173.99 60.61 Blue
92 167.80 73.94 Green
93 170.13 85.02 Grey
94 166.32 78.36 Brown
95 167.40 93.86 Brown
96 173.20 87.66 Brown
97 175.94 88.93 Brown
98 171.57 87.13 Grey
99 175.28 79.88 Brown
100 170.19 72.51 Green
101 173.19 85.26 Green
102 162.68 83.66 Blue
103 160.82 99.96 Green
104 171.76 77.81 Blue
105 175.43 87.48 Green
106 170.68 84.27 Blue
107 166.67 75.58 Blue
108 164.06 88.46 Green
109 180.90 52.16 Green
110 163.54 85.95 Grey
111 165.24 76.95 Brown
112 166.52 61.26 Green
113 160.50 66.79 Blue
114 170.61 75.79 Grey
115 162.91 62.92 Grey
116 174.04 61.28 Green
117 169.44 87.71 Grey
118 182.83 77.76 Blue
119 166.13 89.55 Blue
120 169.79 73.59 Blue
121 154.08 87.52 Grey
122 161.47 74.96 Blue
123 176.09 75.89 Blue
124 170.61 84.36 Brown
125 168.44 82.73 Brown
126 176.28 63.99 Green
127 172.85 89.11 Green
128 163.22 80.97 Grey
129 176.45 90.81 Grey
130 177.64 101.24 Green
131 159.83 91.64 Brown
132 160.61 80.75 Brown
133 170.92 72.41 Brown
134 165.53 71.39 Green
135 181.70 84.27 Brown
136 163.89 66.99 Grey
137 170.91 98.61 Blue
138 171.58 67.32 Blue
139 168.77 84.94 Blue
140 164.69 72.98 Blue
141 170.46 84.62 Brown
142 163.46 76.80 Blue
143 159.64 72.58 Green
144 173.06 73.24 Grey
145 166.39 93.11 Grey
146 167.60 63.56 Grey
147 172.38 76.24 Grey
148 165.48 92.20 Brown
149 160.94 84.55 Brown
150 160.57 66.98 Brown
151 165.86 77.54 Grey
152 168.22 80.44 Grey
153 182.17 75.01 Blue
154 172.55 72.83 Brown
155 155.52 56.67 Green
156 179.76 69.88 Green
157 181.10 85.28 Green
158 162.37 76.94 Blue
159 164.56 95.11 Grey
160 169.41 55.03 Grey
161 169.63 90.04 Blue
162 166.82 77.74 Brown
163 163.30 73.98 Grey
164 165.55 86.53 Green
165 170.52 72.78 Brown
166 159.65 83.54 Grey
167 163.58 74.22 Brown
168 172.16 97.75 Green
169 164.87 73.15 Blue
170 171.96 69.21 Grey
171 169.61 84.53 Green
172 173.73 89.34 Green
173 179.29 95.20 Grey
174 171.01 72.03 Blue
175 169.32 83.16 Blue
176 170.56 84.21 Grey
177 162.23 80.77 Grey
178 176.03 81.20 Grey
179 164.85 90.79 Grey
180 175.75 83.00 Grey
181 167.78 71.54 Green
182 164.76 78.83 Blue
183 165.89 59.43 Brown
184 170.98 86.34 Grey
185 163.53 76.26 Blue
186 175.25 61.72 Grey
187 169.86 74.38 Brown
188 172.98 86.13 Brown
189 167.03 85.10 Green
190 168.84 85.53 Green
191 164.50 83.98 Grey
192 166.29 78.43 Grey
193 168.80 82.74 Blue
194 176.72 92.60 Brown
195 174.93 62.06 Blue
196 163.69 97.37 Grey
197 161.89 73.30 Grey
198 165.11 82.54 Grey
199 165.47 83.51 Blue
200 169.38 77.50 Green
201 172.11 92.16 Brown
202 164.91 64.46 Blue
203 158.68 58.64 Grey
204 177.38 82.41 Blue
205 170.20 83.58 Blue
206 171.04 65.16 Grey
207 156.88 100.93 Green
208 173.03 86.24 Green
209 161.48 66.68 Brown
210 168.44 78.73 Brown
211 166.16 81.23 Blue
212 174.39 71.83 Grey
213 162.56 81.86 Grey
214 164.64 63.46 Green
215 164.82 80.15 Blue
216 167.47 74.81 Grey
217 175.20 85.61 Blue
218 172.49 79.47 Brown
219 165.04 80.50 Brown
220 171.13 69.99 Grey
221 168.72 94.40 Blue
222 165.99 75.55 Blue
223 186.88 75.16 Green
224 163.50 78.57 Blue
225 163.34 93.32 Brown
226 185.93 83.33 Blue
227 170.98 73.47 Green
228 180.51 73.85 Green
229 182.34 77.55 Grey
230 167.14 80.70 Blue
231 175.77 70.76 Green
232 168.87 81.96 Brown
233 176.22 76.95 Brown
234 172.45 63.01 Green
235 176.84 69.19 Blue
236 166.75 71.86 Green
237 167.82 85.98 Grey
238 174.21 74.87 Blue
239 169.58 76.62 Grey
240 171.20 78.76 Grey
241 165.43 69.53 Blue
242 172.04 89.99 Blue
243 171.06 81.67 Blue
244 166.46 49.00 Brown
245 170.14 78.24 Green
246 173.54 67.16 Brown
247 167.69 100.57 Grey
248 171.30 72.61 Grey
249 171.69 63.29 Green
250 169.79 86.47 Blue
251 160.36 101.13 Brown
252 177.19 81.62 Blue
253 177.50 78.27 Brown
254 162.42 74.35 Blue
255 165.87 57.69 Blue
256 168.70 75.45 Blue
257 169.11 94.83 Grey
258 179.59 89.99 Green
259 166.48 85.53 Brown
260 174.02 91.84 Blue
261 169.46 79.78 Grey
262 166.40 73.24 Grey
263 170.69 72.98 Blue
264 174.43 87.46 Grey
265 167.72 75.31 Brown
266 176.36 68.66 Green
267 174.30 75.47 Brown
268 164.83 76.89 Blue
269 167.14 72.55 Blue
270 172.33 85.10 Blue
271 181.88 65.62 Brown
272 170.50 88.14 Brown
273 164.17 84.53 Grey
274 175.14 62.04 Blue
275 169.97 83.76 Blue
276 170.44 85.29 Grey
277 170.29 80.49 Brown
278 163.24 84.12 Brown
279 166.68 81.43 Green
280 167.11 64.48 Green
281 174.48 90.75 Blue
282 162.09 76.50 Green
283 158.56 84.30 Blue
284 169.72 76.01 Green
285 164.97 80.23 Blue
286 175.91 70.07 Grey
287 165.95 76.11 Grey
288 171.58 85.85 Grey
289 178.76 78.31 Grey
290 165.41 82.17 Blue
291 168.74 69.76 Brown
292 177.99 87.84 Brown
293 164.26 73.88 Green
294 167.93 67.50 Blue
295 170.21 93.14 Grey
296 180.01 86.50 Green
297 168.17 73.92 Blue
298 182.43 93.23 Green
299 172.45 84.00 Brown
300 171.47 80.99 Grey
301 170.07 73.18 Blue
302 164.86 80.91 Brown
303 173.12 67.85 Brown
304 181.15 75.42 Blue
305 183.01 75.88 Grey
306 177.64 78.44 Grey
307 167.51 73.48 Green
308 166.28 93.64 Brown
309 159.20 69.54 Grey
310 175.25 75.30 Grey
311 170.74 75.04 Grey
312 178.27 71.12 Blue
313 173.78 79.15 Blue
314 166.96 72.41 Grey
315 173.01 83.71 Blue
316 168.83 91.39 Blue
317 167.49 105.06 Blue
318 180.94 83.86 Blue
319 166.18 67.16 Brown
320 167.34 83.41 Blue
321 177.04 73.81 Brown
322 159.17 72.77 Green
323 159.90 84.25 Brown
324 172.81 74.76 Brown
325 167.05 90.64 Brown
326 161.75 88.13 Brown
327 171.23 90.44 Green
328 169.41 86.81 Blue
329 181.78 71.85 Green
330 170.05 86.16 Blue
331 169.52 92.10 Grey
332 161.82 83.23 Brown
333 162.83 57.08 Blue
334 164.14 83.68 Blue
335 165.52 79.52 Blue
336 172.33 76.05 Brown
337 167.32 75.76 Green
338 166.48 80.42 Green
339 174.71 73.47 Green
340 157.33 70.35 Brown
341 167.72 88.25 Green
342 168.66 74.61 Grey
343 171.99 80.20 Blue
344 166.79 95.70 Brown
345 176.33 77.19 Grey
346 170.19 70.45 Blue
347 175.61 80.09 Grey
348 176.34 98.49 Blue
349 164.62 70.29 Green
350 170.46 76.67 Blue
351 171.80 75.03 Brown
352 165.24 70.47 Grey
353 175.92 96.10 Grey
354 160.41 72.57 Blue
355 168.46 86.45 Green
356 172.26 81.60 Grey
357 172.43 78.87 Blue
358 166.60 64.38 Brown
359 171.98 79.47 Grey
360 173.91 77.91 Grey
361 167.14 72.47 Blue
362 170.28 85.33 Grey
363 165.60 84.56 Blue
364 174.59 89.26 Blue
365 176.49 80.63 Brown
366 173.03 64.72 Blue
367 162.49 101.94 Brown
368 172.66 78.22 Green
369 164.63 87.46 Grey
370 163.43 80.09 Green
371 172.50 104.82 Green
372 178.01 77.68 Grey
373 158.58 79.07 Brown
374 177.60 69.00 Blue
375 164.87 93.10 Green
376 172.25 75.87 Brown
377 168.39 85.00 Grey
378 165.88 88.26 Blue
379 163.99 59.81 Grey
380 167.42 80.20 Grey
381 170.84 79.51 Blue
382 170.14 78.49 Green
383 174.07 85.53 Grey
384 165.19 78.35 Brown
385 177.92 77.66 Brown
386 169.22 80.10 Brown
387 160.95 94.46 Brown
388 170.47 88.17 Blue
389 174.07 54.00 Grey
390 165.35 81.34 Grey
391 163.65 85.27 Grey
392 172.06 78.10 Green
393 167.45 95.23 Green
394 164.83 82.91 Brown
395 165.34 84.14 Blue
396 169.68 91.07 Green
397 171.06 73.10 Blue
398 177.54 81.82 Brown
399 171.05 84.78 Grey
400 183.27 85.35 Grey
401 173.52 69.38 Green
402 163.04 80.80 Green
403 172.29 77.98 Brown
404 169.17 70.42 Grey
405 176.91 62.12 Brown
406 179.48 72.30 Green
407 165.40 81.58 Brown
408 169.35 63.70 Blue
409 174.55 83.57 Green
410 170.63 85.54 Brown
411 184.04 62.70 Grey
412 157.71 82.48 Green
413 169.53 63.98 Grey
414 176.03 78.67 Grey
415 163.35 77.29 Grey
416 179.83 94.24 Blue
417 179.91 83.00 Green
418 172.09 83.43 Green
419 171.07 71.62 Green
420 171.68 72.52 Blue
421 174.11 83.64 Grey
422 174.07 83.11 Green
423 164.32 95.12 Green
424 165.36 75.19 Grey
425 183.54 76.18 Grey
426 166.59 79.87 Green
427 169.17 85.52 Grey
428 172.66 79.81 Grey
429 162.76 59.67 Brown
430 167.26 85.85 Blue
431 165.83 76.07 Brown
432 173.98 70.31 Grey
433 174.43 92.54 Brown
434 166.46 75.74 Brown
435 169.47 80.54 Brown
436 159.40 69.90 Green
437 162.27 84.98 Blue
438 178.47 95.22 Brown
439 171.12 66.56 Blue
440 166.80 72.28 Brown
441 170.25 87.38 Green
442 178.95 84.96 Blue
443 169.32 84.61 Grey
444 173.68 81.01 Green
445 163.71 75.20 Blue
446 167.66 83.94 Grey
447 165.91 80.02 Brown
448 174.19 73.30 Green
449 174.43 70.99 Green
450 164.22 68.77 Green
451 172.62 75.15 Green
452 172.57 82.23 Green
453 164.40 85.43 Grey
454 169.81 77.90 Green
455 171.83 98.82 Brown
456 163.09 92.71 Grey
457 171.92 86.73 Green
458 166.74 70.05 Brown
459 168.52 81.00 Green
460 173.61 57.68 Grey
461 160.95 77.60 Green
462 167.85 75.70 Blue
463 169.00 92.42 Green
464 160.74 74.91 Blue
465 162.35 87.52 Green
466 160.55 66.73 Brown
467 169.28 70.93 Grey
468 174.59 93.14 Brown
469 166.68 65.47 Grey
470 171.54 88.60 Blue
471 173.31 61.09 Brown
472 177.92 80.40 Brown
473 169.90 70.63 Blue
474 173.49 70.67 Blue
475 175.82 73.43 Brown
476 165.05 79.28 Brown
477 171.31 74.54 Green
478 178.47 91.19 Blue
479 164.64 80.38 Blue
480 175.35 87.09 Green
481 171.35 83.70 Green
482 169.41 79.74 Blue
483 172.61 71.74 Blue
484 166.31 84.03 Grey
485 173.11 81.61 Grey
486 166.20 72.73 Green
487 168.61 87.52 Green
488 168.91 71.30 Blue
489 164.92 97.75 Brown
490 161.20 80.50 Brown
491 179.20 89.28 Grey
492 173.23 73.13 Green
493 173.87 53.02 Blue
494 178.80 86.57 Grey
495 171.80 63.51 Green
496 168.85 69.94 Grey
497 173.01 85.65 Blue
498 179.18 69.09 Blue
499 168.06 60.29 Grey
500 180.39 80.42 Blue
501 166.09 70.00 Brown
502 164.27 83.28 Blue
503 162.78 96.37 Green
504 173.90 63.69 Blue
505 168.65 69.12 Blue
506 173.78 77.70 Green
507 176.22 60.02 Blue
508 157.87 68.66 Brown
509 177.85 71.33 Grey
510 161.27 79.90 Green
511 175.57 87.16 Blue
512 163.13 87.26 Brown
513 162.73 76.72 Green
514 162.13 82.49 Green
515 166.14 79.34 Green
516 171.63 91.17 Grey
517 170.59 91.92 Brown
518 163.96 80.56 Grey
519 161.30 69.06 Blue
520 164.64 77.07 Grey
521 174.14 92.51 Brown
522 170.39 88.56 Green
523 165.57 67.47 Grey
524 169.65 55.15 Blue
525 155.03 91.23 Blue
526 175.91 86.25 Brown
527 183.54 79.93 Green
528 169.92 91.06 Brown
529 169.43 68.86 Blue
530 166.30 83.50 Blue
531 171.86 75.66 Blue
532 171.87 67.37 Brown
533 177.43 88.34 Brown
534 176.08 82.56 Green
535 167.49 70.98 Brown
536 168.70 71.84 Blue
537 176.66 80.84 Blue
538 168.10 84.78 Grey
539 168.13 71.18 Green
540 174.16 77.50 Green
541 178.16 74.43 Green
542 174.07 87.70 Grey
543 165.33 77.90 Green
544 162.01 93.90 Green
545 165.04 69.86 Green
546 166.74 69.35 Blue
547 175.98 58.45 Blue
548 176.16 60.18 Blue
549 167.14 84.86 Brown
550 172.55 66.26 Green
551 163.07 86.61 Brown
552 173.56 84.87 Grey
553 169.22 76.37 Brown
554 168.34 80.76 Grey
555 174.06 83.56 Blue
556 173.87 84.33 Grey
557 181.65 82.39 Green
558 174.31 80.20 Brown
559 171.64 69.87 Green
560 165.92 88.66 Grey
561 173.09 85.24 Brown
562 170.02 95.55 Brown
563 160.37 71.20 Blue
564 166.35 82.99 Green
565 175.14 72.39 Grey
566 168.72 94.47 Green
567 165.52 81.78 Brown
568 171.44 72.69 Brown
569 169.52 75.70 Blue
570 167.48 64.07 Grey
571 170.98 84.10 Blue
572 174.73 84.10 Blue
573 168.71 81.11 Brown
574 165.68 75.43 Blue
575 177.56 100.71 Grey
576 179.76 76.61 Green
577 172.34 74.14 Brown
578 170.94 81.92 Blue
579 167.17 77.16 Green
580 165.47 75.14 Brown
581 173.20 90.95 Blue
582 175.76 85.36 Grey
583 170.23 80.31 Green
584 170.03 81.58 Blue
585 174.85 60.39 Green
586 161.46 83.62 Green
587 168.15 98.94 Green
588 167.20 78.05 Green
589 174.49 83.32 Grey
590 166.83 84.53 Brown
591 173.33 88.22 Brown
592 166.87 78.61 Grey
593 184.69 82.95 Blue
594 161.64 70.24 Brown
595 169.85 91.73 Brown
596 165.39 72.80 Brown
597 164.38 73.67 Blue
598 173.09 75.31 Green
599 164.81 72.55 Blue
600 165.92 73.29 Green
601 167.22 67.00 Green
602 167.51 59.64 Brown
603 176.52 81.19 Grey
604 168.38 74.29 Blue
605 171.48 89.26 Green
606 173.68 91.88 Blue
607 172.11 83.37 Green
608 179.57 64.81 Green
609 166.83 78.68 Grey
610 173.29 92.84 Green
611 164.38 82.61 Grey
612 169.88 86.74 Blue
613 180.42 53.66 Brown
614 157.72 68.74 Grey
615 169.05 87.71 Green
616 175.82 61.64 Green
617 175.01 81.52 Blue
618 166.29 93.73 Green
619 169.69 63.50 Grey
620 176.04 75.54 Brown
621 173.98 86.66 Blue
622 180.77 73.43 Grey
623 174.85 76.07 Blue
624 170.22 93.88 Brown
625 169.93 84.33 Blue
626 162.29 92.40 Grey
627 159.75 74.69 Brown
628 165.48 79.01 Brown
629 153.30 75.80 Grey
630 160.11 77.49 Blue
631 167.16 79.78 Blue
632 174.23 56.20 Green
633 173.16 77.77 Blue
634 175.20 96.03 Brown
635 175.81 81.37 Grey
636 169.48 80.39 Blue
637 163.38 42.44 Brown
638 176.22 84.04 Grey
639 160.96 84.52 Grey
640 169.75 86.11 Blue
641 169.77 86.47 Blue
642 169.38 74.21 Brown
643 163.52 84.15 Brown
644 169.56 82.20 Brown
645 156.12 81.25 Brown
646 163.12 88.32 Grey
647 173.91 86.68 Blue
648 176.51 74.95 Grey
649 162.02 91.63 Brown
650 166.33 85.08 Grey
651 188.50 97.90 Grey
652 165.69 72.99 Brown
653 176.44 70.73 Brown
654 175.39 68.60 Brown
655 166.57 76.25 Grey
656 167.34 95.45 Grey
657 173.98 75.11 Blue
658 174.89 78.76 Blue
659 163.61 76.38 Blue
660 181.64 68.89 Green
661 168.93 81.73 Green
662 163.45 75.59 Brown
663 164.65 74.39 Brown
664 159.85 82.07 Green
665 167.30 68.70 Brown
666 168.00 81.63 Brown
667 178.06 65.05 Green
668 168.39 55.44 Grey
669 161.51 81.70 Green
670 169.99 73.31 Blue
671 162.54 76.31 Brown
672 167.34 76.80 Blue
673 169.77 85.44 Brown
674 162.94 69.60 Green
675 179.24 74.27 Blue
676 175.40 75.11 Green
677 166.90 86.47 Green
678 176.51 74.67 Brown
679 173.71 77.54 Green
680 165.25 76.65 Blue
681 169.57 67.23 Green
682 172.70 80.34 Blue
683 167.91 69.57 Blue
684 164.37 71.98 Grey
685 163.32 87.98 Brown
686 178.25 64.58 Green
687 173.12 88.53 Brown
688 163.42 98.42 Brown
689 173.29 71.93 Grey
690 166.56 80.73 Blue
691 172.20 78.21 Brown
692 172.65 67.41 Blue
693 159.35 74.75 Brown
694 161.80 75.35 Green
695 174.64 72.16 Blue
696 168.52 71.68 Grey
697 174.80 70.11 Blue
698 172.30 74.12 Green
699 166.11 80.49 Green
700 170.01 86.89 Green
701 167.11 83.14 Grey
702 165.84 82.58 Green
703 163.15 72.28 Green
704 173.18 71.18 Green
705 179.22 82.31 Brown
706 171.93 88.47 Green
707 167.72 68.18 Grey
708 154.86 82.13 Blue
709 157.08 95.09 Blue
710 175.47 83.29 Grey
711 170.77 98.06 Blue
712 177.26 63.03 Grey
713 170.17 83.16 Blue
714 174.37 93.05 Green
715 175.32 92.86 Green
716 169.51 84.44 Grey
717 178.32 94.22 Grey
718 163.04 76.15 Brown
719 179.64 68.95 Brown
720 167.63 92.46 Grey
721 167.20 67.52 Blue
722 178.36 77.12 Brown
723 170.14 75.68 Blue
724 177.09 67.08 Grey
725 165.37 77.82 Grey
726 173.09 87.06 Grey
727 173.15 90.03 Brown
728 169.60 84.10 Blue
729 172.21 74.26 Blue
730 163.93 69.61 Brown
731 174.62 79.59 Blue
732 160.85 72.51 Grey
733 178.99 84.93 Green
734 156.30 80.16 Blue
735 166.73 89.29 Green
736 177.39 78.60 Brown
737 172.92 71.02 Grey
738 171.37 78.44 Brown
739 172.44 88.50 Green
740 169.27 74.64 Brown
741 159.90 80.26 Brown
742 173.71 71.87 Green
743 178.91 83.63 Grey
744 171.43 79.69 Brown
745 176.50 81.05 Blue
746 158.25 87.90 Blue
747 171.18 85.29 Blue
748 171.80 78.18 Blue
749 158.96 75.69 Brown
750 173.75 86.03 Brown
751 169.29 83.85 Green
752 167.07 77.65 Green
753 174.17 96.27 Brown
754 173.10 71.50 Green
755 177.04 70.49 Brown
756 167.10 96.18 Brown
757 170.23 70.73 Grey
758 156.21 87.79 Brown
759 163.14 86.02 Green
760 172.41 75.10 Blue
761 159.97 75.53 Grey
762 171.28 71.84 Green
763 171.06 86.83 Brown
764 161.86 84.20 Green
765 172.86 81.48 Grey
766 174.60 71.85 Blue
767 174.53 71.21 Brown
768 166.09 78.19 Brown
769 181.43 87.44 Green
770 171.31 79.93 Brown
771 173.16 74.37 Brown
772 174.45 77.42 Brown
773 173.31 80.81 Blue
774 168.07 60.33 Green
775 168.23 55.50 Green
776 167.24 88.01 Brown
777 163.15 82.89 Brown
778 169.22 67.35 Blue
779 178.10 74.11 Green
780 159.89 75.57 Blue
781 166.01 78.82 Grey
782 174.70 75.29 Grey
783 174.81 98.82 Brown
784 172.47 88.51 Brown
785 167.58 69.25 Green
786 171.69 88.26 Blue
787 177.76 83.45 Blue
788 168.67 70.41 Green
789 168.26 60.83 Grey
790 173.50 85.12 Green
791 177.81 96.89 Blue
792 170.98 81.66 Grey
793 172.35 105.41 Green
794 168.57 91.74 Green
795 168.71 80.16 Green
796 171.50 73.56 Green
797 182.57 74.85 Blue
798 160.90 66.12 Blue
799 161.17 78.51 Green
800 174.67 93.00 Blue
801 167.78 93.57 Green
802 176.25 82.35 Grey
803 165.85 88.39 Blue
804 163.32 61.41 Blue
805 168.02 78.21 Brown
806 173.14 78.49 Brown
807 182.40 78.46 Brown
808 169.72 97.62 Green
809 163.45 74.31 Grey
810 157.42 65.91 Blue
811 165.78 69.89 Blue
812 161.71 61.65 Green
813 164.90 73.15 Grey
814 169.84 73.79 Grey
815 170.36 66.49 Brown
816 176.86 53.91 Blue
817 181.38 78.90 Grey
818 167.77 71.28 Grey
819 166.33 94.56 Brown
820 164.72 61.61 Grey
821 179.16 92.64 Green
822 161.60 77.58 Grey
823 166.23 89.33 Grey
824 166.43 77.34 Grey
825 180.26 84.34 Green
826 173.70 88.84 Grey
827 170.26 68.87 Brown
828 169.83 97.88 Brown
829 167.86 77.35 Blue
830 165.15 63.92 Blue
831 178.85 80.43 Blue
832 170.63 75.64 Green
833 162.62 98.04 Blue
834 181.44 73.80 Grey
835 179.05 71.00 Brown
836 169.65 87.66 Grey
837 172.31 80.88 Blue
838 174.65 77.59 Grey
839 171.56 88.78 Blue
840 160.99 86.84 Green
841 170.68 84.01 Brown
842 166.95 71.35 Blue
843 166.81 78.04 Brown
844 166.38 80.38 Blue
845 183.45 73.12 Blue
846 165.79 60.01 Grey
847 168.91 78.28 Brown
848 165.55 73.65 Brown
849 179.08 69.47 Brown
850 179.24 84.05 Blue
851 175.73 72.09 Grey
852 170.25 89.80 Blue
853 171.48 87.51 Green
854 168.00 89.85 Grey
855 163.96 66.13 Blue
856 174.10 79.85 Green
857 168.62 71.37 Grey
858 163.50 79.41 Blue
859 168.49 76.89 Grey
860 175.44 78.58 Blue
861 161.11 82.00 Brown
862 173.82 90.02 Grey
863 167.46 69.76 Grey
864 165.96 84.76 Grey
865 168.92 75.98 Green
866 171.48 65.92 Blue
867 168.96 72.85 Brown
868 176.34 70.25 Blue
869 162.91 74.55 Green
870 174.90 70.69 Blue
871 171.19 94.46 Grey
872 167.28 83.77 Blue
873 173.43 72.47 Grey
874 167.45 92.39 Grey
875 169.31 81.41 Brown
876 174.46 83.55 Grey
877 175.35 93.75 Green
878 167.73 88.64 Blue
879 174.27 85.11 Green
880 165.67 91.20 Brown
881 170.69 87.70 Grey
882 163.92 74.03 Blue
883 169.82 95.14 Brown
884 183.98 94.25 Blue
885 158.96 54.55 Green
886 164.55 74.34 Grey
887 185.40 73.50 Brown
888 172.33 91.02 Blue
889 163.77 64.76 Blue
890 165.66 82.46 Grey
891 168.98 70.71 Grey
892 167.02 87.14 Brown
893 176.57 71.40 Brown
894 170.99 65.24 Grey
895 166.24 84.30 Brown
896 163.34 86.98 Blue
897 178.25 64.66 Green
898 178.23 68.99 Brown
899 163.50 87.35 Brown
900 159.42 89.44 Green
901 174.45 72.26 Blue
902 173.58 76.70 Brown
903 165.62 101.53 Blue
904 159.73 83.79 Green
905 169.26 82.65 Blue
906 165.61 80.21 Blue
907 175.45 74.12 Green
908 177.55 86.17 Blue
909 172.72 83.37 Green
910 174.96 63.90 Grey
911 155.64 77.06 Blue
912 177.74 96.05 Grey
913 163.57 68.77 Brown
914 171.93 88.31 Brown
915 179.54 77.79 Brown
916 183.08 59.64 Green
917 177.74 74.41 Blue
918 166.41 71.92 Brown
919 166.01 90.04 Grey
920 162.21 74.12 Grey
921 166.44 76.14 Green
922 168.11 84.90 Brown
923 168.14 60.27 Blue
924 162.55 81.20 Blue
925 170.70 62.72 Brown
926 172.61 83.05 Blue
927 169.06 95.84 Grey
928 176.27 84.34 Grey
929 164.07 83.32 Blue
930 163.36 82.26 Green
931 178.37 58.12 Grey
932 178.93 56.88 Grey
933 165.29 82.88 Green
934 179.90 78.90 Brown
935 170.55 84.33 Green
936 172.39 92.11 Grey
937 170.24 63.83 Grey
938 180.18 97.43 Brown
939 173.49 78.19 Green
940 170.59 85.51 Green
941 172.91 78.75 Brown
942 167.57 69.00 Blue
943 161.75 57.53 Brown
944 170.31 76.96 Blue
945 170.95 60.48 Brown
946 169.49 66.04 Brown
947 178.16 80.19 Brown
948 173.19 59.54 Grey
949 171.36 80.12 Green
950 173.53 86.19 Brown
951 170.85 94.67 Blue
952 172.80 83.82 Grey
953 166.47 80.09 Grey
954 161.10 75.71 Green
955 157.51 84.77 Grey
956 166.98 71.83 Grey
957 177.54 74.07 Blue
958 172.63 78.52 Green
959 174.26 76.36 Grey
960 169.81 84.28 Brown
961 163.34 78.71 Brown
962 165.57 88.54 Brown
963 174.36 57.76 Blue
964 164.74 80.72 Grey
965 163.74 64.39 Blue
966 183.82 86.70 Brown
967 168.25 78.99 Brown
968 170.16 72.08 Green
969 168.56 90.43 Blue
970 168.45 67.01 Grey
971 171.10 91.09 Grey
972 173.34 85.12 Grey
973 175.60 64.25 Grey
974 163.92 90.06 Green
975 173.20 84.09 Blue
976 167.12 59.46 Green
977 164.89 87.36 Grey
978 166.75 95.99 Grey
979 173.98 83.10 Grey
980 167.26 91.68 Brown
981 164.63 85.98 Brown
982 161.01 77.78 Brown
983 166.48 59.29 Brown
984 175.68 83.80 Blue
985 171.94 78.71 Brown
986 167.59 73.30 Grey
987 172.48 51.64 Grey
988 165.61 99.19 Brown
989 168.76 63.30 Blue
990 178.97 67.85 Grey
991 169.19 83.71 Grey
992 163.64 66.78 Green
993 168.05 68.92 Grey
994 165.81 82.35 Blue
995 182.89 76.94 Brown
996 170.22 87.93 Green
997 168.26 77.28 Green
998 183.32 86.77 Brown
999 164.68 75.10 Blue
1000 168.12 81.68 Grey

Random assignment

I’m now going to flip (an imaginary, computer-generated) coin for each of these 1,000 individuals to assigned them to group A or B:

ID Height Weight Eye colour Group
1 168.09 88.99 Blue A
2 167.65 79.18 Brown A
3 177.98 57.43 Grey A
4 165.78 75.69 Green B
5 169.25 88.53 Grey B
6 168.13 69.16 Green A
7 163.46 82.53 Grey A
8 162.71 63.50 Green A
9 162.37 79.47 Grey A
10 167.73 78.13 Blue A
11 183.98 90.12 Blue B
12 170.65 80.77 Grey A
13 172.10 100.08 Green A
14 164.96 75.34 Brown A
15 168.50 93.14 Brown B
16 178.37 85.26 Grey B
17 170.71 84.51 Blue B
18 171.52 70.54 Grey B
19 174.60 81.44 Green B
20 168.50 90.35 Grey A
21 168.14 60.92 Grey A
22 164.56 85.65 Grey A
23 169.44 72.09 Grey B
24 180.33 75.69 Brown A
25 169.95 86.88 Brown B
26 177.57 88.34 Green A
27 169.01 70.70 Green A
28 176.60 93.62 Blue A
29 165.24 76.34 Green A
30 165.62 66.87 Grey A
31 180.71 83.29 Blue B
32 167.76 72.33 Green B
33 157.26 71.70 Blue B
34 156.54 103.45 Blue A
35 165.18 80.55 Green B
36 168.49 81.54 Grey A
37 160.43 60.27 Grey A
38 178.23 75.10 Green B
39 180.80 94.18 Grey A
40 178.17 100.40 Blue B
41 173.13 83.90 Blue B
42 169.71 74.63 Blue A
43 172.65 91.93 Grey B
44 174.95 88.44 Blue A
45 170.61 79.57 Brown A
46 165.23 90.13 Grey A
47 176.94 80.02 Green A
48 160.80 76.57 Blue A
49 165.69 73.29 Blue A
50 167.15 82.52 Blue B
51 176.00 68.63 Grey B
52 165.45 82.08 Green A
53 156.10 89.26 Grey A
54 175.13 71.62 Blue B
55 153.53 81.37 Brown A
56 169.54 81.90 Green B
57 165.12 79.77 Blue A
58 157.54 83.71 Green A
59 160.74 77.19 Grey A
60 161.55 90.73 Brown B
61 171.25 64.53 Brown B
62 169.39 83.20 Brown A
63 175.46 90.05 Brown B
64 165.66 88.24 Blue B
65 154.86 91.06 Brown B
66 175.14 79.75 Grey A
67 159.96 70.15 Blue B
68 179.79 83.41 Green B
69 164.54 85.69 Grey A
70 174.96 83.22 Green A
71 164.30 92.07 Brown A
72 177.54 69.04 Brown A
73 176.04 87.41 Brown B
74 170.89 83.72 Grey A
75 158.89 78.55 Grey A
76 164.74 69.47 Grey A
77 161.98 101.60 Grey A
78 169.34 68.99 Brown B
79 169.99 93.26 Grey B
80 164.39 71.53 Green A
81 174.02 90.99 Brown A
82 171.57 80.53 Grey B
83 171.25 83.25 Blue A
84 174.18 75.49 Blue A
85 171.26 73.02 Green B
86 166.76 91.66 Green B
87 172.64 71.37 Blue A
88 167.76 75.99 Green B
89 167.86 60.90 Grey B
90 167.38 98.61 Brown B
91 173.99 60.61 Blue A
92 167.80 73.94 Green A
93 170.13 85.02 Grey A
94 166.32 78.36 Brown B
95 167.40 93.86 Brown A
96 173.20 87.66 Brown A
97 175.94 88.93 Brown B
98 171.57 87.13 Grey A
99 175.28 79.88 Brown B
100 170.19 72.51 Green A
101 173.19 85.26 Green A
102 162.68 83.66 Blue B
103 160.82 99.96 Green B
104 171.76 77.81 Blue A
105 175.43 87.48 Green A
106 170.68 84.27 Blue B
107 166.67 75.58 Blue B
108 164.06 88.46 Green B
109 180.90 52.16 Green A
110 163.54 85.95 Grey A
111 165.24 76.95 Brown B
112 166.52 61.26 Green B
113 160.50 66.79 Blue A
114 170.61 75.79 Grey A
115 162.91 62.92 Grey B
116 174.04 61.28 Green B
117 169.44 87.71 Grey B
118 182.83 77.76 Blue B
119 166.13 89.55 Blue A
120 169.79 73.59 Blue B
121 154.08 87.52 Grey A
122 161.47 74.96 Blue B
123 176.09 75.89 Blue B
124 170.61 84.36 Brown A
125 168.44 82.73 Brown A
126 176.28 63.99 Green B
127 172.85 89.11 Green A
128 163.22 80.97 Grey B
129 176.45 90.81 Grey B
130 177.64 101.24 Green B
131 159.83 91.64 Brown B
132 160.61 80.75 Brown A
133 170.92 72.41 Brown A
134 165.53 71.39 Green A
135 181.70 84.27 Brown B
136 163.89 66.99 Grey A
137 170.91 98.61 Blue A
138 171.58 67.32 Blue A
139 168.77 84.94 Blue A
140 164.69 72.98 Blue A
141 170.46 84.62 Brown B
142 163.46 76.80 Blue B
143 159.64 72.58 Green B
144 173.06 73.24 Grey B
145 166.39 93.11 Grey B
146 167.60 63.56 Grey B
147 172.38 76.24 Grey A
148 165.48 92.20 Brown A
149 160.94 84.55 Brown B
150 160.57 66.98 Brown B
151 165.86 77.54 Grey B
152 168.22 80.44 Grey B
153 182.17 75.01 Blue B
154 172.55 72.83 Brown B
155 155.52 56.67 Green A
156 179.76 69.88 Green B
157 181.10 85.28 Green B
158 162.37 76.94 Blue B
159 164.56 95.11 Grey A
160 169.41 55.03 Grey A
161 169.63 90.04 Blue B
162 166.82 77.74 Brown A
163 163.30 73.98 Grey A
164 165.55 86.53 Green B
165 170.52 72.78 Brown A
166 159.65 83.54 Grey A
167 163.58 74.22 Brown A
168 172.16 97.75 Green B
169 164.87 73.15 Blue B
170 171.96 69.21 Grey B
171 169.61 84.53 Green B
172 173.73 89.34 Green A
173 179.29 95.20 Grey B
174 171.01 72.03 Blue B
175 169.32 83.16 Blue A
176 170.56 84.21 Grey A
177 162.23 80.77 Grey B
178 176.03 81.20 Grey B
179 164.85 90.79 Grey A
180 175.75 83.00 Grey A
181 167.78 71.54 Green A
182 164.76 78.83 Blue A
183 165.89 59.43 Brown A
184 170.98 86.34 Grey A
185 163.53 76.26 Blue A
186 175.25 61.72 Grey B
187 169.86 74.38 Brown B
188 172.98 86.13 Brown A
189 167.03 85.10 Green B
190 168.84 85.53 Green A
191 164.50 83.98 Grey A
192 166.29 78.43 Grey B
193 168.80 82.74 Blue B
194 176.72 92.60 Brown B
195 174.93 62.06 Blue B
196 163.69 97.37 Grey A
197 161.89 73.30 Grey B
198 165.11 82.54 Grey A
199 165.47 83.51 Blue A
200 169.38 77.50 Green A
201 172.11 92.16 Brown A
202 164.91 64.46 Blue A
203 158.68 58.64 Grey A
204 177.38 82.41 Blue A
205 170.20 83.58 Blue A
206 171.04 65.16 Grey B
207 156.88 100.93 Green A
208 173.03 86.24 Green A
209 161.48 66.68 Brown A
210 168.44 78.73 Brown B
211 166.16 81.23 Blue B
212 174.39 71.83 Grey A
213 162.56 81.86 Grey B
214 164.64 63.46 Green A
215 164.82 80.15 Blue B
216 167.47 74.81 Grey A
217 175.20 85.61 Blue B
218 172.49 79.47 Brown B
219 165.04 80.50 Brown A
220 171.13 69.99 Grey A
221 168.72 94.40 Blue A
222 165.99 75.55 Blue A
223 186.88 75.16 Green A
224 163.50 78.57 Blue B
225 163.34 93.32 Brown B
226 185.93 83.33 Blue B
227 170.98 73.47 Green B
228 180.51 73.85 Green A
229 182.34 77.55 Grey A
230 167.14 80.70 Blue B
231 175.77 70.76 Green B
232 168.87 81.96 Brown A
233 176.22 76.95 Brown A
234 172.45 63.01 Green A
235 176.84 69.19 Blue B
236 166.75 71.86 Green B
237 167.82 85.98 Grey A
238 174.21 74.87 Blue B
239 169.58 76.62 Grey B
240 171.20 78.76 Grey A
241 165.43 69.53 Blue A
242 172.04 89.99 Blue A
243 171.06 81.67 Blue B
244 166.46 49.00 Brown B
245 170.14 78.24 Green A
246 173.54 67.16 Brown B
247 167.69 100.57 Grey A
248 171.30 72.61 Grey A
249 171.69 63.29 Green B
250 169.79 86.47 Blue B
251 160.36 101.13 Brown A
252 177.19 81.62 Blue B
253 177.50 78.27 Brown B
254 162.42 74.35 Blue B
255 165.87 57.69 Blue A
256 168.70 75.45 Blue A
257 169.11 94.83 Grey A
258 179.59 89.99 Green A
259 166.48 85.53 Brown B
260 174.02 91.84 Blue B
261 169.46 79.78 Grey A
262 166.40 73.24 Grey A
263 170.69 72.98 Blue A
264 174.43 87.46 Grey B
265 167.72 75.31 Brown B
266 176.36 68.66 Green B
267 174.30 75.47 Brown A
268 164.83 76.89 Blue A
269 167.14 72.55 Blue B
270 172.33 85.10 Blue B
271 181.88 65.62 Brown A
272 170.50 88.14 Brown A
273 164.17 84.53 Grey A
274 175.14 62.04 Blue B
275 169.97 83.76 Blue A
276 170.44 85.29 Grey B
277 170.29 80.49 Brown A
278 163.24 84.12 Brown B
279 166.68 81.43 Green B
280 167.11 64.48 Green A
281 174.48 90.75 Blue B
282 162.09 76.50 Green A
283 158.56 84.30 Blue A
284 169.72 76.01 Green B
285 164.97 80.23 Blue A
286 175.91 70.07 Grey B
287 165.95 76.11 Grey B
288 171.58 85.85 Grey B
289 178.76 78.31 Grey A
290 165.41 82.17 Blue B
291 168.74 69.76 Brown B
292 177.99 87.84 Brown A
293 164.26 73.88 Green A
294 167.93 67.50 Blue B
295 170.21 93.14 Grey A
296 180.01 86.50 Green A
297 168.17 73.92 Blue B
298 182.43 93.23 Green A
299 172.45 84.00 Brown B
300 171.47 80.99 Grey B
301 170.07 73.18 Blue A
302 164.86 80.91 Brown B
303 173.12 67.85 Brown A
304 181.15 75.42 Blue A
305 183.01 75.88 Grey A
306 177.64 78.44 Grey A
307 167.51 73.48 Green B
308 166.28 93.64 Brown B
309 159.20 69.54 Grey B
310 175.25 75.30 Grey B
311 170.74 75.04 Grey A
312 178.27 71.12 Blue A
313 173.78 79.15 Blue A
314 166.96 72.41 Grey B
315 173.01 83.71 Blue B
316 168.83 91.39 Blue A
317 167.49 105.06 Blue B
318 180.94 83.86 Blue A
319 166.18 67.16 Brown B
320 167.34 83.41 Blue A
321 177.04 73.81 Brown B
322 159.17 72.77 Green A
323 159.90 84.25 Brown B
324 172.81 74.76 Brown B
325 167.05 90.64 Brown A
326 161.75 88.13 Brown B
327 171.23 90.44 Green B
328 169.41 86.81 Blue A
329 181.78 71.85 Green A
330 170.05 86.16 Blue A
331 169.52 92.10 Grey A
332 161.82 83.23 Brown A
333 162.83 57.08 Blue B
334 164.14 83.68 Blue B
335 165.52 79.52 Blue A
336 172.33 76.05 Brown B
337 167.32 75.76 Green A
338 166.48 80.42 Green A
339 174.71 73.47 Green B
340 157.33 70.35 Brown A
341 167.72 88.25 Green A
342 168.66 74.61 Grey A
343 171.99 80.20 Blue A
344 166.79 95.70 Brown A
345 176.33 77.19 Grey A
346 170.19 70.45 Blue A
347 175.61 80.09 Grey A
348 176.34 98.49 Blue A
349 164.62 70.29 Green B
350 170.46 76.67 Blue A
351 171.80 75.03 Brown A
352 165.24 70.47 Grey A
353 175.92 96.10 Grey B
354 160.41 72.57 Blue A
355 168.46 86.45 Green B
356 172.26 81.60 Grey B
357 172.43 78.87 Blue A
358 166.60 64.38 Brown A
359 171.98 79.47 Grey A
360 173.91 77.91 Grey B
361 167.14 72.47 Blue A
362 170.28 85.33 Grey B
363 165.60 84.56 Blue B
364 174.59 89.26 Blue B
365 176.49 80.63 Brown B
366 173.03 64.72 Blue A
367 162.49 101.94 Brown B
368 172.66 78.22 Green B
369 164.63 87.46 Grey B
370 163.43 80.09 Green A
371 172.50 104.82 Green A
372 178.01 77.68 Grey B
373 158.58 79.07 Brown A
374 177.60 69.00 Blue B
375 164.87 93.10 Green B
376 172.25 75.87 Brown A
377 168.39 85.00 Grey A
378 165.88 88.26 Blue A
379 163.99 59.81 Grey A
380 167.42 80.20 Grey A
381 170.84 79.51 Blue B
382 170.14 78.49 Green A
383 174.07 85.53 Grey B
384 165.19 78.35 Brown A
385 177.92 77.66 Brown B
386 169.22 80.10 Brown A
387 160.95 94.46 Brown B
388 170.47 88.17 Blue B
389 174.07 54.00 Grey A
390 165.35 81.34 Grey A
391 163.65 85.27 Grey B
392 172.06 78.10 Green A
393 167.45 95.23 Green A
394 164.83 82.91 Brown B
395 165.34 84.14 Blue A
396 169.68 91.07 Green A
397 171.06 73.10 Blue A
398 177.54 81.82 Brown A
399 171.05 84.78 Grey B
400 183.27 85.35 Grey A
401 173.52 69.38 Green B
402 163.04 80.80 Green A
403 172.29 77.98 Brown A
404 169.17 70.42 Grey B
405 176.91 62.12 Brown B
406 179.48 72.30 Green B
407 165.40 81.58 Brown A
408 169.35 63.70 Blue A
409 174.55 83.57 Green B
410 170.63 85.54 Brown B
411 184.04 62.70 Grey B
412 157.71 82.48 Green B
413 169.53 63.98 Grey B
414 176.03 78.67 Grey A
415 163.35 77.29 Grey B
416 179.83 94.24 Blue A
417 179.91 83.00 Green B
418 172.09 83.43 Green B
419 171.07 71.62 Green B
420 171.68 72.52 Blue B
421 174.11 83.64 Grey A
422 174.07 83.11 Green A
423 164.32 95.12 Green A
424 165.36 75.19 Grey A
425 183.54 76.18 Grey B
426 166.59 79.87 Green B
427 169.17 85.52 Grey A
428 172.66 79.81 Grey B
429 162.76 59.67 Brown A
430 167.26 85.85 Blue A
431 165.83 76.07 Brown B
432 173.98 70.31 Grey B
433 174.43 92.54 Brown A
434 166.46 75.74 Brown B
435 169.47 80.54 Brown A
436 159.40 69.90 Green A
437 162.27 84.98 Blue B
438 178.47 95.22 Brown A
439 171.12 66.56 Blue A
440 166.80 72.28 Brown A
441 170.25 87.38 Green A
442 178.95 84.96 Blue A
443 169.32 84.61 Grey B
444 173.68 81.01 Green A
445 163.71 75.20 Blue A
446 167.66 83.94 Grey B
447 165.91 80.02 Brown A
448 174.19 73.30 Green B
449 174.43 70.99 Green A
450 164.22 68.77 Green A
451 172.62 75.15 Green B
452 172.57 82.23 Green A
453 164.40 85.43 Grey B
454 169.81 77.90 Green A
455 171.83 98.82 Brown A
456 163.09 92.71 Grey B
457 171.92 86.73 Green B
458 166.74 70.05 Brown A
459 168.52 81.00 Green B
460 173.61 57.68 Grey A
461 160.95 77.60 Green A
462 167.85 75.70 Blue B
463 169.00 92.42 Green A
464 160.74 74.91 Blue B
465 162.35 87.52 Green A
466 160.55 66.73 Brown A
467 169.28 70.93 Grey B
468 174.59 93.14 Brown B
469 166.68 65.47 Grey B
470 171.54 88.60 Blue B
471 173.31 61.09 Brown B
472 177.92 80.40 Brown A
473 169.90 70.63 Blue A
474 173.49 70.67 Blue A
475 175.82 73.43 Brown B
476 165.05 79.28 Brown A
477 171.31 74.54 Green B
478 178.47 91.19 Blue B
479 164.64 80.38 Blue A
480 175.35 87.09 Green B
481 171.35 83.70 Green A
482 169.41 79.74 Blue A
483 172.61 71.74 Blue B
484 166.31 84.03 Grey A
485 173.11 81.61 Grey B
486 166.20 72.73 Green B
487 168.61 87.52 Green B
488 168.91 71.30 Blue B
489 164.92 97.75 Brown A
490 161.20 80.50 Brown A
491 179.20 89.28 Grey B
492 173.23 73.13 Green A
493 173.87 53.02 Blue A
494 178.80 86.57 Grey A
495 171.80 63.51 Green A
496 168.85 69.94 Grey B
497 173.01 85.65 Blue A
498 179.18 69.09 Blue B
499 168.06 60.29 Grey B
500 180.39 80.42 Blue B
501 166.09 70.00 Brown A
502 164.27 83.28 Blue A
503 162.78 96.37 Green A
504 173.90 63.69 Blue B
505 168.65 69.12 Blue B
506 173.78 77.70 Green A
507 176.22 60.02 Blue A
508 157.87 68.66 Brown A
509 177.85 71.33 Grey A
510 161.27 79.90 Green B
511 175.57 87.16 Blue A
512 163.13 87.26 Brown A
513 162.73 76.72 Green A
514 162.13 82.49 Green B
515 166.14 79.34 Green B
516 171.63 91.17 Grey A
517 170.59 91.92 Brown A
518 163.96 80.56 Grey A
519 161.30 69.06 Blue B
520 164.64 77.07 Grey A
521 174.14 92.51 Brown A
522 170.39 88.56 Green A
523 165.57 67.47 Grey B
524 169.65 55.15 Blue A
525 155.03 91.23 Blue A
526 175.91 86.25 Brown B
527 183.54 79.93 Green A
528 169.92 91.06 Brown A
529 169.43 68.86 Blue B
530 166.30 83.50 Blue B
531 171.86 75.66 Blue A
532 171.87 67.37 Brown A
533 177.43 88.34 Brown B
534 176.08 82.56 Green A
535 167.49 70.98 Brown B
536 168.70 71.84 Blue B
537 176.66 80.84 Blue B
538 168.10 84.78 Grey B
539 168.13 71.18 Green A
540 174.16 77.50 Green A
541 178.16 74.43 Green A
542 174.07 87.70 Grey A
543 165.33 77.90 Green A
544 162.01 93.90 Green A
545 165.04 69.86 Green B
546 166.74 69.35 Blue B
547 175.98 58.45 Blue A
548 176.16 60.18 Blue A
549 167.14 84.86 Brown B
550 172.55 66.26 Green A
551 163.07 86.61 Brown A
552 173.56 84.87 Grey B
553 169.22 76.37 Brown B
554 168.34 80.76 Grey A
555 174.06 83.56 Blue A
556 173.87 84.33 Grey B
557 181.65 82.39 Green A
558 174.31 80.20 Brown B
559 171.64 69.87 Green B
560 165.92 88.66 Grey A
561 173.09 85.24 Brown B
562 170.02 95.55 Brown B
563 160.37 71.20 Blue B
564 166.35 82.99 Green B
565 175.14 72.39 Grey B
566 168.72 94.47 Green B
567 165.52 81.78 Brown A
568 171.44 72.69 Brown B
569 169.52 75.70 Blue B
570 167.48 64.07 Grey B
571 170.98 84.10 Blue A
572 174.73 84.10 Blue B
573 168.71 81.11 Brown A
574 165.68 75.43 Blue A
575 177.56 100.71 Grey B
576 179.76 76.61 Green B
577 172.34 74.14 Brown B
578 170.94 81.92 Blue A
579 167.17 77.16 Green A
580 165.47 75.14 Brown B
581 173.20 90.95 Blue B
582 175.76 85.36 Grey A
583 170.23 80.31 Green B
584 170.03 81.58 Blue A
585 174.85 60.39 Green B
586 161.46 83.62 Green B
587 168.15 98.94 Green B
588 167.20 78.05 Green A
589 174.49 83.32 Grey B
590 166.83 84.53 Brown B
591 173.33 88.22 Brown B
592 166.87 78.61 Grey A
593 184.69 82.95 Blue A
594 161.64 70.24 Brown A
595 169.85 91.73 Brown A
596 165.39 72.80 Brown A
597 164.38 73.67 Blue B
598 173.09 75.31 Green A
599 164.81 72.55 Blue B
600 165.92 73.29 Green B
601 167.22 67.00 Green A
602 167.51 59.64 Brown A
603 176.52 81.19 Grey B
604 168.38 74.29 Blue B
605 171.48 89.26 Green B
606 173.68 91.88 Blue B
607 172.11 83.37 Green B
608 179.57 64.81 Green A
609 166.83 78.68 Grey B
610 173.29 92.84 Green A
611 164.38 82.61 Grey A
612 169.88 86.74 Blue B
613 180.42 53.66 Brown B
614 157.72 68.74 Grey B
615 169.05 87.71 Green A
616 175.82 61.64 Green B
617 175.01 81.52 Blue B
618 166.29 93.73 Green A
619 169.69 63.50 Grey B
620 176.04 75.54 Brown B
621 173.98 86.66 Blue B
622 180.77 73.43 Grey A
623 174.85 76.07 Blue A
624 170.22 93.88 Brown A
625 169.93 84.33 Blue B
626 162.29 92.40 Grey A
627 159.75 74.69 Brown A
628 165.48 79.01 Brown B
629 153.30 75.80 Grey B
630 160.11 77.49 Blue B
631 167.16 79.78 Blue B
632 174.23 56.20 Green A
633 173.16 77.77 Blue A
634 175.20 96.03 Brown B
635 175.81 81.37 Grey B
636 169.48 80.39 Blue A
637 163.38 42.44 Brown B
638 176.22 84.04 Grey A
639 160.96 84.52 Grey B
640 169.75 86.11 Blue A
641 169.77 86.47 Blue B
642 169.38 74.21 Brown A
643 163.52 84.15 Brown A
644 169.56 82.20 Brown A
645 156.12 81.25 Brown A
646 163.12 88.32 Grey A
647 173.91 86.68 Blue A
648 176.51 74.95 Grey A
649 162.02 91.63 Brown B
650 166.33 85.08 Grey A
651 188.50 97.90 Grey A
652 165.69 72.99 Brown B
653 176.44 70.73 Brown B
654 175.39 68.60 Brown B
655 166.57 76.25 Grey B
656 167.34 95.45 Grey B
657 173.98 75.11 Blue B
658 174.89 78.76 Blue A
659 163.61 76.38 Blue A
660 181.64 68.89 Green B
661 168.93 81.73 Green A
662 163.45 75.59 Brown B
663 164.65 74.39 Brown B
664 159.85 82.07 Green A
665 167.30 68.70 Brown B
666 168.00 81.63 Brown A
667 178.06 65.05 Green B
668 168.39 55.44 Grey A
669 161.51 81.70 Green A
670 169.99 73.31 Blue A
671 162.54 76.31 Brown A
672 167.34 76.80 Blue B
673 169.77 85.44 Brown B
674 162.94 69.60 Green B
675 179.24 74.27 Blue A
676 175.40 75.11 Green A
677 166.90 86.47 Green B
678 176.51 74.67 Brown B
679 173.71 77.54 Green A
680 165.25 76.65 Blue A
681 169.57 67.23 Green B
682 172.70 80.34 Blue A
683 167.91 69.57 Blue A
684 164.37 71.98 Grey B
685 163.32 87.98 Brown A
686 178.25 64.58 Green B
687 173.12 88.53 Brown A
688 163.42 98.42 Brown A
689 173.29 71.93 Grey A
690 166.56 80.73 Blue A
691 172.20 78.21 Brown A
692 172.65 67.41 Blue A
693 159.35 74.75 Brown A
694 161.80 75.35 Green B
695 174.64 72.16 Blue B
696 168.52 71.68 Grey B
697 174.80 70.11 Blue A
698 172.30 74.12 Green A
699 166.11 80.49 Green B
700 170.01 86.89 Green B
701 167.11 83.14 Grey A
702 165.84 82.58 Green B
703 163.15 72.28 Green A
704 173.18 71.18 Green A
705 179.22 82.31 Brown A
706 171.93 88.47 Green B
707 167.72 68.18 Grey A
708 154.86 82.13 Blue A
709 157.08 95.09 Blue A
710 175.47 83.29 Grey B
711 170.77 98.06 Blue A
712 177.26 63.03 Grey A
713 170.17 83.16 Blue A
714 174.37 93.05 Green A
715 175.32 92.86 Green B
716 169.51 84.44 Grey A
717 178.32 94.22 Grey A
718 163.04 76.15 Brown A
719 179.64 68.95 Brown A
720 167.63 92.46 Grey A
721 167.20 67.52 Blue A
722 178.36 77.12 Brown B
723 170.14 75.68 Blue A
724 177.09 67.08 Grey B
725 165.37 77.82 Grey A
726 173.09 87.06 Grey B
727 173.15 90.03 Brown B
728 169.60 84.10 Blue B
729 172.21 74.26 Blue A
730 163.93 69.61 Brown A
731 174.62 79.59 Blue A
732 160.85 72.51 Grey A
733 178.99 84.93 Green A
734 156.30 80.16 Blue A
735 166.73 89.29 Green B
736 177.39 78.60 Brown B
737 172.92 71.02 Grey A
738 171.37 78.44 Brown A
739 172.44 88.50 Green B
740 169.27 74.64 Brown A
741 159.90 80.26 Brown B
742 173.71 71.87 Green A
743 178.91 83.63 Grey A
744 171.43 79.69 Brown A
745 176.50 81.05 Blue A
746 158.25 87.90 Blue B
747 171.18 85.29 Blue A
748 171.80 78.18 Blue A
749 158.96 75.69 Brown B
750 173.75 86.03 Brown B
751 169.29 83.85 Green A
752 167.07 77.65 Green B
753 174.17 96.27 Brown A
754 173.10 71.50 Green A
755 177.04 70.49 Brown B
756 167.10 96.18 Brown B
757 170.23 70.73 Grey A
758 156.21 87.79 Brown B
759 163.14 86.02 Green B
760 172.41 75.10 Blue B
761 159.97 75.53 Grey A
762 171.28 71.84 Green A
763 171.06 86.83 Brown B
764 161.86 84.20 Green A
765 172.86 81.48 Grey A
766 174.60 71.85 Blue B
767 174.53 71.21 Brown A
768 166.09 78.19 Brown A
769 181.43 87.44 Green A
770 171.31 79.93 Brown B
771 173.16 74.37 Brown A
772 174.45 77.42 Brown A
773 173.31 80.81 Blue A
774 168.07 60.33 Green B
775 168.23 55.50 Green A
776 167.24 88.01 Brown B
777 163.15 82.89 Brown B
778 169.22 67.35 Blue B
779 178.10 74.11 Green A
780 159.89 75.57 Blue B
781 166.01 78.82 Grey B
782 174.70 75.29 Grey B
783 174.81 98.82 Brown B
784 172.47 88.51 Brown A
785 167.58 69.25 Green A
786 171.69 88.26 Blue B
787 177.76 83.45 Blue A
788 168.67 70.41 Green A
789 168.26 60.83 Grey B
790 173.50 85.12 Green A
791 177.81 96.89 Blue B
792 170.98 81.66 Grey B
793 172.35 105.41 Green B
794 168.57 91.74 Green B
795 168.71 80.16 Green B
796 171.50 73.56 Green B
797 182.57 74.85 Blue A
798 160.90 66.12 Blue B
799 161.17 78.51 Green A
800 174.67 93.00 Blue A
801 167.78 93.57 Green A
802 176.25 82.35 Grey B
803 165.85 88.39 Blue A
804 163.32 61.41 Blue B
805 168.02 78.21 Brown A
806 173.14 78.49 Brown A
807 182.40 78.46 Brown A
808 169.72 97.62 Green B
809 163.45 74.31 Grey B
810 157.42 65.91 Blue A
811 165.78 69.89 Blue B
812 161.71 61.65 Green B
813 164.90 73.15 Grey A
814 169.84 73.79 Grey B
815 170.36 66.49 Brown B
816 176.86 53.91 Blue B
817 181.38 78.90 Grey B
818 167.77 71.28 Grey B
819 166.33 94.56 Brown A
820 164.72 61.61 Grey B
821 179.16 92.64 Green B
822 161.60 77.58 Grey A
823 166.23 89.33 Grey B
824 166.43 77.34 Grey B
825 180.26 84.34 Green A
826 173.70 88.84 Grey B
827 170.26 68.87 Brown B
828 169.83 97.88 Brown A
829 167.86 77.35 Blue B
830 165.15 63.92 Blue A
831 178.85 80.43 Blue B
832 170.63 75.64 Green B
833 162.62 98.04 Blue B
834 181.44 73.80 Grey B
835 179.05 71.00 Brown B
836 169.65 87.66 Grey B
837 172.31 80.88 Blue B
838 174.65 77.59 Grey B
839 171.56 88.78 Blue B
840 160.99 86.84 Green A
841 170.68 84.01 Brown A
842 166.95 71.35 Blue B
843 166.81 78.04 Brown B
844 166.38 80.38 Blue B
845 183.45 73.12 Blue A
846 165.79 60.01 Grey B
847 168.91 78.28 Brown A
848 165.55 73.65 Brown B
849 179.08 69.47 Brown B
850 179.24 84.05 Blue B
851 175.73 72.09 Grey A
852 170.25 89.80 Blue B
853 171.48 87.51 Green B
854 168.00 89.85 Grey A
855 163.96 66.13 Blue A
856 174.10 79.85 Green A
857 168.62 71.37 Grey A
858 163.50 79.41 Blue A
859 168.49 76.89 Grey A
860 175.44 78.58 Blue A
861 161.11 82.00 Brown B
862 173.82 90.02 Grey A
863 167.46 69.76 Grey B
864 165.96 84.76 Grey B
865 168.92 75.98 Green A
866 171.48 65.92 Blue A
867 168.96 72.85 Brown A
868 176.34 70.25 Blue B
869 162.91 74.55 Green A
870 174.90 70.69 Blue B
871 171.19 94.46 Grey B
872 167.28 83.77 Blue B
873 173.43 72.47 Grey A
874 167.45 92.39 Grey B
875 169.31 81.41 Brown A
876 174.46 83.55 Grey B
877 175.35 93.75 Green B
878 167.73 88.64 Blue B
879 174.27 85.11 Green A
880 165.67 91.20 Brown B
881 170.69 87.70 Grey A
882 163.92 74.03 Blue A
883 169.82 95.14 Brown B
884 183.98 94.25 Blue B
885 158.96 54.55 Green A
886 164.55 74.34 Grey B
887 185.40 73.50 Brown B
888 172.33 91.02 Blue B
889 163.77 64.76 Blue A
890 165.66 82.46 Grey B
891 168.98 70.71 Grey B
892 167.02 87.14 Brown B
893 176.57 71.40 Brown B
894 170.99 65.24 Grey A
895 166.24 84.30 Brown A
896 163.34 86.98 Blue A
897 178.25 64.66 Green A
898 178.23 68.99 Brown A
899 163.50 87.35 Brown A
900 159.42 89.44 Green A
901 174.45 72.26 Blue B
902 173.58 76.70 Brown B
903 165.62 101.53 Blue A
904 159.73 83.79 Green A
905 169.26 82.65 Blue A
906 165.61 80.21 Blue B
907 175.45 74.12 Green B
908 177.55 86.17 Blue A
909 172.72 83.37 Green B
910 174.96 63.90 Grey A
911 155.64 77.06 Blue B
912 177.74 96.05 Grey A
913 163.57 68.77 Brown B
914 171.93 88.31 Brown A
915 179.54 77.79 Brown A
916 183.08 59.64 Green B
917 177.74 74.41 Blue A
918 166.41 71.92 Brown A
919 166.01 90.04 Grey A
920 162.21 74.12 Grey B
921 166.44 76.14 Green B
922 168.11 84.90 Brown B
923 168.14 60.27 Blue B
924 162.55 81.20 Blue B
925 170.70 62.72 Brown B
926 172.61 83.05 Blue A
927 169.06 95.84 Grey B
928 176.27 84.34 Grey B
929 164.07 83.32 Blue A
930 163.36 82.26 Green B
931 178.37 58.12 Grey A
932 178.93 56.88 Grey A
933 165.29 82.88 Green A
934 179.90 78.90 Brown B
935 170.55 84.33 Green A
936 172.39 92.11 Grey A
937 170.24 63.83 Grey A
938 180.18 97.43 Brown A
939 173.49 78.19 Green B
940 170.59 85.51 Green A
941 172.91 78.75 Brown B
942 167.57 69.00 Blue A
943 161.75 57.53 Brown A
944 170.31 76.96 Blue B
945 170.95 60.48 Brown A
946 169.49 66.04 Brown A
947 178.16 80.19 Brown A
948 173.19 59.54 Grey A
949 171.36 80.12 Green A
950 173.53 86.19 Brown B
951 170.85 94.67 Blue A
952 172.80 83.82 Grey B
953 166.47 80.09 Grey B
954 161.10 75.71 Green A
955 157.51 84.77 Grey A
956 166.98 71.83 Grey B
957 177.54 74.07 Blue A
958 172.63 78.52 Green A
959 174.26 76.36 Grey A
960 169.81 84.28 Brown A
961 163.34 78.71 Brown A
962 165.57 88.54 Brown A
963 174.36 57.76 Blue B
964 164.74 80.72 Grey A
965 163.74 64.39 Blue B
966 183.82 86.70 Brown A
967 168.25 78.99 Brown A
968 170.16 72.08 Green A
969 168.56 90.43 Blue A
970 168.45 67.01 Grey B
971 171.10 91.09 Grey B
972 173.34 85.12 Grey B
973 175.60 64.25 Grey B
974 163.92 90.06 Green A
975 173.20 84.09 Blue A
976 167.12 59.46 Green B
977 164.89 87.36 Grey A
978 166.75 95.99 Grey B
979 173.98 83.10 Grey B
980 167.26 91.68 Brown A
981 164.63 85.98 Brown B
982 161.01 77.78 Brown B
983 166.48 59.29 Brown A
984 175.68 83.80 Blue A
985 171.94 78.71 Brown B
986 167.59 73.30 Grey A
987 172.48 51.64 Grey B
988 165.61 99.19 Brown A
989 168.76 63.30 Blue B
990 178.97 67.85 Grey B
991 169.19 83.71 Grey B
992 163.64 66.78 Green B
993 168.05 68.92 Grey A
994 165.81 82.35 Blue A
995 182.89 76.94 Brown B
996 170.22 87.93 Green B
997 168.26 77.28 Green A
998 183.32 86.77 Brown B
999 164.68 75.10 Blue A
1000 168.12 81.68 Grey B

How similar are these groups?

Let’s first check their heights:

How similar are these groups?

And their weights:

How similar are these groups?

And their eye colors:

Making sure this wasn’t a fluke

Let’s re-run this:

ID Height Weight Eye colour Group
1 168.09 88.99 Blue B
2 167.65 79.18 Brown B
3 177.98 57.43 Grey A
4 165.78 75.69 Green B
5 169.25 88.53 Grey A
6 168.13 69.16 Green A
7 163.46 82.53 Grey B
8 162.71 63.50 Green B
9 162.37 79.47 Grey A
10 167.73 78.13 Blue B
11 183.98 90.12 Blue B
12 170.65 80.77 Grey B
13 172.10 100.08 Green A
14 164.96 75.34 Brown A
15 168.50 93.14 Brown A
16 178.37 85.26 Grey A
17 170.71 84.51 Blue A
18 171.52 70.54 Grey B
19 174.60 81.44 Green B
20 168.50 90.35 Grey A
21 168.14 60.92 Grey A
22 164.56 85.65 Grey B
23 169.44 72.09 Grey B
24 180.33 75.69 Brown B
25 169.95 86.88 Brown A
26 177.57 88.34 Green B
27 169.01 70.70 Green A
28 176.60 93.62 Blue A
29 165.24 76.34 Green B
30 165.62 66.87 Grey A
31 180.71 83.29 Blue B
32 167.76 72.33 Green B
33 157.26 71.70 Blue B
34 156.54 103.45 Blue A
35 165.18 80.55 Green A
36 168.49 81.54 Grey B
37 160.43 60.27 Grey A
38 178.23 75.10 Green B
39 180.80 94.18 Grey B
40 178.17 100.40 Blue B
41 173.13 83.90 Blue B
42 169.71 74.63 Blue A
43 172.65 91.93 Grey B
44 174.95 88.44 Blue B
45 170.61 79.57 Brown A
46 165.23 90.13 Grey A
47 176.94 80.02 Green A
48 160.80 76.57 Blue B
49 165.69 73.29 Blue B
50 167.15 82.52 Blue B
51 176.00 68.63 Grey A
52 165.45 82.08 Green B
53 156.10 89.26 Grey B
54 175.13 71.62 Blue B
55 153.53 81.37 Brown B
56 169.54 81.90 Green A
57 165.12 79.77 Blue B
58 157.54 83.71 Green A
59 160.74 77.19 Grey B
60 161.55 90.73 Brown A
61 171.25 64.53 Brown B
62 169.39 83.20 Brown B
63 175.46 90.05 Brown B
64 165.66 88.24 Blue B
65 154.86 91.06 Brown B
66 175.14 79.75 Grey A
67 159.96 70.15 Blue A
68 179.79 83.41 Green B
69 164.54 85.69 Grey B
70 174.96 83.22 Green B
71 164.30 92.07 Brown B
72 177.54 69.04 Brown B
73 176.04 87.41 Brown A
74 170.89 83.72 Grey A
75 158.89 78.55 Grey A
76 164.74 69.47 Grey B
77 161.98 101.60 Grey A
78 169.34 68.99 Brown A
79 169.99 93.26 Grey B
80 164.39 71.53 Green B
81 174.02 90.99 Brown A
82 171.57 80.53 Grey A
83 171.25 83.25 Blue A
84 174.18 75.49 Blue B
85 171.26 73.02 Green A
86 166.76 91.66 Green B
87 172.64 71.37 Blue A
88 167.76 75.99 Green B
89 167.86 60.90 Grey B
90 167.38 98.61 Brown B
91 173.99 60.61 Blue B
92 167.80 73.94 Green B
93 170.13 85.02 Grey A
94 166.32 78.36 Brown B
95 167.40 93.86 Brown A
96 173.20 87.66 Brown B
97 175.94 88.93 Brown A
98 171.57 87.13 Grey B
99 175.28 79.88 Brown A
100 170.19 72.51 Green B
101 173.19 85.26 Green B
102 162.68 83.66 Blue A
103 160.82 99.96 Green B
104 171.76 77.81 Blue A
105 175.43 87.48 Green A
106 170.68 84.27 Blue B
107 166.67 75.58 Blue B
108 164.06 88.46 Green B
109 180.90 52.16 Green B
110 163.54 85.95 Grey B
111 165.24 76.95 Brown B
112 166.52 61.26 Green B
113 160.50 66.79 Blue B
114 170.61 75.79 Grey A
115 162.91 62.92 Grey B
116 174.04 61.28 Green B
117 169.44 87.71 Grey A
118 182.83 77.76 Blue A
119 166.13 89.55 Blue B
120 169.79 73.59 Blue B
121 154.08 87.52 Grey B
122 161.47 74.96 Blue B
123 176.09 75.89 Blue A
124 170.61 84.36 Brown B
125 168.44 82.73 Brown A
126 176.28 63.99 Green B
127 172.85 89.11 Green B
128 163.22 80.97 Grey A
129 176.45 90.81 Grey A
130 177.64 101.24 Green A
131 159.83 91.64 Brown B
132 160.61 80.75 Brown A
133 170.92 72.41 Brown B
134 165.53 71.39 Green A
135 181.70 84.27 Brown B
136 163.89 66.99 Grey A
137 170.91 98.61 Blue A
138 171.58 67.32 Blue A
139 168.77 84.94 Blue A
140 164.69 72.98 Blue B
141 170.46 84.62 Brown B
142 163.46 76.80 Blue A
143 159.64 72.58 Green B
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811 165.78 69.89 Blue B
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816 176.86 53.91 Blue A
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837 172.31 80.88 Blue A
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845 183.45 73.12 Blue B
846 165.79 60.01 Grey B
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848 165.55 73.65 Brown A
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852 170.25 89.80 Blue B
853 171.48 87.51 Green B
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855 163.96 66.13 Blue B
856 174.10 79.85 Green A
857 168.62 71.37 Grey A
858 163.50 79.41 Blue B
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860 175.44 78.58 Blue A
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866 171.48 65.92 Blue B
867 168.96 72.85 Brown B
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875 169.31 81.41 Brown A
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877 175.35 93.75 Green B
878 167.73 88.64 Blue A
879 174.27 85.11 Green A
880 165.67 91.20 Brown B
881 170.69 87.70 Grey A
882 163.92 74.03 Blue A
883 169.82 95.14 Brown A
884 183.98 94.25 Blue A
885 158.96 54.55 Green A
886 164.55 74.34 Grey A
887 185.40 73.50 Brown B
888 172.33 91.02 Blue B
889 163.77 64.76 Blue A
890 165.66 82.46 Grey B
891 168.98 70.71 Grey B
892 167.02 87.14 Brown A
893 176.57 71.40 Brown A
894 170.99 65.24 Grey B
895 166.24 84.30 Brown A
896 163.34 86.98 Blue B
897 178.25 64.66 Green B
898 178.23 68.99 Brown B
899 163.50 87.35 Brown A
900 159.42 89.44 Green A
901 174.45 72.26 Blue B
902 173.58 76.70 Brown B
903 165.62 101.53 Blue A
904 159.73 83.79 Green A
905 169.26 82.65 Blue B
906 165.61 80.21 Blue A
907 175.45 74.12 Green A
908 177.55 86.17 Blue A
909 172.72 83.37 Green B
910 174.96 63.90 Grey A
911 155.64 77.06 Blue A
912 177.74 96.05 Grey B
913 163.57 68.77 Brown A
914 171.93 88.31 Brown B
915 179.54 77.79 Brown B
916 183.08 59.64 Green B
917 177.74 74.41 Blue B
918 166.41 71.92 Brown A
919 166.01 90.04 Grey A
920 162.21 74.12 Grey A
921 166.44 76.14 Green A
922 168.11 84.90 Brown B
923 168.14 60.27 Blue A
924 162.55 81.20 Blue A
925 170.70 62.72 Brown A
926 172.61 83.05 Blue A
927 169.06 95.84 Grey A
928 176.27 84.34 Grey B
929 164.07 83.32 Blue A
930 163.36 82.26 Green A
931 178.37 58.12 Grey B
932 178.93 56.88 Grey A
933 165.29 82.88 Green B
934 179.90 78.90 Brown B
935 170.55 84.33 Green A
936 172.39 92.11 Grey A
937 170.24 63.83 Grey B
938 180.18 97.43 Brown A
939 173.49 78.19 Green B
940 170.59 85.51 Green B
941 172.91 78.75 Brown B
942 167.57 69.00 Blue B
943 161.75 57.53 Brown A
944 170.31 76.96 Blue B
945 170.95 60.48 Brown B
946 169.49 66.04 Brown B
947 178.16 80.19 Brown A
948 173.19 59.54 Grey B
949 171.36 80.12 Green A
950 173.53 86.19 Brown B
951 170.85 94.67 Blue A
952 172.80 83.82 Grey B
953 166.47 80.09 Grey B
954 161.10 75.71 Green B
955 157.51 84.77 Grey B
956 166.98 71.83 Grey A
957 177.54 74.07 Blue B
958 172.63 78.52 Green A
959 174.26 76.36 Grey B
960 169.81 84.28 Brown A
961 163.34 78.71 Brown A
962 165.57 88.54 Brown B
963 174.36 57.76 Blue B
964 164.74 80.72 Grey B
965 163.74 64.39 Blue A
966 183.82 86.70 Brown B
967 168.25 78.99 Brown B
968 170.16 72.08 Green A
969 168.56 90.43 Blue A
970 168.45 67.01 Grey B
971 171.10 91.09 Grey A
972 173.34 85.12 Grey A
973 175.60 64.25 Grey A
974 163.92 90.06 Green A
975 173.20 84.09 Blue B
976 167.12 59.46 Green B
977 164.89 87.36 Grey B
978 166.75 95.99 Grey B
979 173.98 83.10 Grey A
980 167.26 91.68 Brown A
981 164.63 85.98 Brown A
982 161.01 77.78 Brown A
983 166.48 59.29 Brown B
984 175.68 83.80 Blue B
985 171.94 78.71 Brown A
986 167.59 73.30 Grey B
987 172.48 51.64 Grey A
988 165.61 99.19 Brown A
989 168.76 63.30 Blue A
990 178.97 67.85 Grey B
991 169.19 83.71 Grey B
992 163.64 66.78 Green A
993 168.05 68.92 Grey B
994 165.81 82.35 Blue B
995 182.89 76.94 Brown B
996 170.22 87.93 Green A
997 168.26 77.28 Green B
998 183.32 86.77 Brown A
999 164.68 75.10 Blue A
1000 168.12 81.68 Grey B

Check how similar they are

Increasingly similar

In fact, if we did this many, many, many times, these groups would be, on average, increasingly identical!

Why?

  • Central limit theorem

  • Law of large numbers

Do international monitors deter election-day fraud?

Yes!

  • The international community monitored the 2003 Armenian Presidential elections
  • Monitors were assigned randomly to the polling stations
  • Hyde found a big average difference between the vote share received by the cheating party at monitored stations compared to non-monitored stations.